Here and elsewhere in §24.10 the symbol denotes a prime number.
where the summation is over all such that divides . The denominator of is the product of all these primes .
where , and is an arbitrary integer such that . Here and elsewhere two rational numbers are congruent if the modulus divides the numerator of their difference.
valid when and , where is a fixed integer.
where is a prime and .
valid for fixed integers , and for all and such that .
Let , with and relatively prime and . Then
where and are integers, with relatively prime to .
For historical notes, generalizations, and applications, see Porubský (1998).
With as in §24.10(iii)
valid for fixed integers , and for all such that and .
valid for fixed integers and for all such that .